1 The neoclassical maximization hypothesis

Transcription

1 LAWRENCE A. BOLAND 1 The neoclassical maximization hypothesis At present the maximization postulate has an unusually strong hold on the mind set of economists... Suffice it to say that in my view the belief in favor of maximization does not depend on strong evidence that people are in fact maximizers... The main argument against the maximization postulate is an empirical one namely, people frequently do not maximize. Of course, this standpoint argues that while postulates simplify reality, we are not free to choose counterfactual postulates. Hence, from this point of view a superior postulate would be one under which maximizing behavior is a special case, but non-maximization is accommodated for as a frequent mode of behavior. Harvey Leibenstein [1979, pp ] If by rational we mean demonstrably optimal, it follows that conduct in order to be rational must be relevantly fully informed. George Shackle [1972, p. 125] The assumption of maximization may also place a heavy (often unbearable) computational burden on the decision maker. Herbert Simon [1987, p. 267] The assumption of maximization is a salient feature of every neoclassical explanation. Obviously, then, if one wanted to criticize neoclassical economics it would seem that the most direct way would be to criticize the assumption of universal maximization. Several approaches have been taken. Harvey Leibenstein [1979] offered an external criticism. He argued for a micro-micro theory on the grounds that profit maximization is not necessarily the objective of the actual decision-makers in a firm and that a complete explanation would require an explanation of intrafirm behaviour. He also gave arguments for why maximization of anything may not be realistic or is at best a special case. Similarly, Herbert Simon has argued that individuals do not actually maximize anything they satisfice and

2 12 Principles of economics LAWRENCE A. BOLAND The neoclassical maximization hypothesis 13 yet they still make decisions. 1And of course, George Shackle has for many THE LOGICAL BASIS FOR CRITICISM years argued that maximization is not even possible. As stated above, there are two types of direct criticism of the maximization Some anti-neoclassical economists are very encouraged by these hypothesis: the possibilities criticism and the empirical criticism. In this arguments, but I think these arguments are unsuccessful. For anyone section I will examine the logical bases of these critiques, namely of the opposed to neoclassical theory, a misdirected criticism, which by its failure possibilities argument which concerns only the necessary conditions and of only adds apparent credibility to neoclassical theory, will be worse than the the empirical argument which concerns only the statements which form the absence of criticism. The purpose of this chapter is to explain why, sufficient conditions. In each case I will also discuss the possible logical although the neoclassical hypothesis is not a tautology and thus may be defense for these criticisms. false, no criticism of that hypothesis will ever be successful. My arguments will be based first on the possible types of theoretical criticism and the logic of those criticisms, and second on the methodological status of the The possibilities critique: can the necessary conditions be fulfilled? maximization hypothesis in neoclassical explanations. The possibilities critique builds on the difference between necessary and sufficient conditions. Specifically, what is criticized is the possibility of TYPES OF CRITICISM AND THE MAXIMIZATION fulfilling all of the necessary conditions for maximization. Of course, this HYPOTHESIS type of critique begs the question as to what are all the necessary conditions. Are there more conditions than the (a) and (b) listed above? There are only two types of direct criticism of any behavioural hypothesis Shackle, following Friedrich Hayek and John Maynard Keynes, argues that once its logical validity has been established. One can argue against the maximization also presumes that the knowledge necessary for the process possibility of the hypothesized behaviour or one can argue against the of choosing the best alternative has been acquired. 4 For Shackle, empirical truth of the premise of the hypothesis. In the case of the maximization is always a deliberate act. Shackle argues that for neoclassical maximization hypothesis, virtually everyone accepts the maximization to be a behavioural hypothesis (i.e. about the behaviour of logical validity of the hypothesis. For example, everyone can accept that if decision-makers), the actor must have acquired all of the information the consumer is a utility maximizer, then for the particular bundle of goods necessary to determine or calculate which alternative maximizes utility (or chosen: (a) the marginal utility is zero, and (b) the slope of the marginal profit, etc.) and he argues that such an acquisition is impossible, hence utility curve at the point representing the chosen bundle is non-positive and 2 deliberate maximization is an impossible act. usually negative. That is to say, necessarily the marginal increment to the Although this argument appears to be quite strong, it is rather objective must be zero and falling (or not rising) whenever (i.e. without elementary. A closer examination will show it to be overly optimistic exception) the maximization premise is actually true. Of course, one could because it is epistemologically presumptive. One needs to ask: Why is the substitute the word profit for the word utility and the logic of the possession of the necessary knowledge impossible? This question clearly hypothesis still holds. With either form, (a) and (b) are the necessary involves one s epistemology that is, one s theory of knowledge. The conditions for maximization. Note again that there are no sufficient answer, I think, is quite simple. Shackle s argument (also Hayek s and conditions for maximization. Rather, the maximization premise is the Keynes ) presumes that the truth of one s knowledge requires an inductive sufficient condition for (a) and (b). proof. And as everyone surely knows today, there is no way to prove one s Parenthetically, I should note that economists often refer to the knowledge inductively whenever the amount of information is finite or it is conjunction of (a) and (b) as a sufficient condition for maximization. This otherwise incomplete (e.g. information about the future). 5 is a common error. 3 Even if (a) and (b) are both true, only local The strength of Shackle s argument is actually rather vulnerable. maximization is assured. However, maximization in general (i.e. global) is Inductive proofs (and hence inductive logic) are not necessary for true what the premise explicitly asserts and that is not assured by (a) and (b) knowledge. One s knowledge (i.e. one s theory) can be true even though alone. I will return to this below when I discuss the methodological uses of one does not know it to be true that is, even if one does not have proof. the maximization hypothesis. But I think there is an even stronger objection to the true knowledge is necessary for maximization argument. True knowledge is not necessary

3 14 Principles of economics LAWRENCE A. BOLAND The neoclassical maximization hypothesis 15 for maximization! Consumers, for example, only have to think that their The methodological problems of empirical refutations of economic theory of what is the shape of their utility function is true. Once a consumer theories are widely accepted. In the case of utility maximization we realize picks the best option there is no reason to deviate or engage in that survey reports are suspect and direct observations of the decision- disequilibrium behaviour unless he or she is prone to testing his or her making process are difficult or impossible. In this sense behavioural own theories. 6 maximization is not directly testable. The only objective part of the In summary, Shackle s inductivist argument against the possibility of a maximization hypothesis is the set of logical consequences such as the true maximization hypothesis is a failure. Inductive proofs are not uniquely determinate choices. One might thus attempt an indirect test of necessary for true knowledge and true knowledge (by any means) is not maximization by examining the outcomes of maximization, namely the necessary for successful or determinate decision-making. Maximizing implied pattern of observable choices based on a presumption that there is a behaviour cannot be ruled out as a logical impossibility. utility function and that utility is being maximized by the choices made. If one wishes to avoid errors in logic, an indirect test of any behavioural The empirical critiques: are the sufficient premises true? hypothesis which is based on a direct examination of its logical consequences must be limited to attempting refutations of one or more of Simon and Leibenstein argue against the maximization hypothesis in a the necessary conditions for the truth of the hypothesis. For example, in the more straightforward way. While accepting the logical validity of the case of consumer theory, whenever utility maximization is the basis of hypothesis, they simply deny the truth of the premise of the hypothesis. observed choices, a necessary condition is that for any given pattern of They would allow that if the consumer is actually a maximizer, the choices the Slutsky Theorem must hold. 8 It might appear then that the hypothesis would be a true explanation of the consumer s behaviour but above methodological problems of observation could be easily overcome, they say the premise is false; consumers are not necessarily maximizers since the Slutsky Theorem can in principle be made to involve only hence their behaviour (e.g. their demand) would not necessarily be observable quantities and prices. And, if one could refute the Slutsky determinable on that basis. Leibenstein may allow that the consumer s Theorem then one could indirectly refute the maximization hypothesis. 9 behaviour can be determined, but it is an open question as to what is the Unfortunately, even if from this perspective such an indirect refutation determining factor utility, prestige, social convention, etc.? Simon seems cannot be ruled out on logical grounds alone, the methodological problems to reject as well the necessity of determinate explanation although he does concerning observations will remain. discuss alternative decision rules to substitute for the maximization rule. 7 The fundamental methodological problem of refuting any behavioural A denial of the maximization hypothesis on empirical grounds raises the hypothesis indirectly is that of constructing a convincing refutation. Any obvious question: How do the critics know the premise is false? Certain indirect test of the utility maximization hypothesis will be futile if it is to methodological considerations would seem to give an advantage to the be based on a test of any logically derived implication (such as the Slutsky critics over those who argue in its favour. Note that we can distinguish Theorem). On the one hand, everyone even critics of maximization will between those statements which are verifiable (i.e. when true, can be accept the theorem s logical validity. On the other hand, given the proven true) and those which are refutable (i.e. when false, can be proven numerous constraints involved in any concrete situation, the problems of false) on purely logical grounds. Furthermore, strictly universal statements observation will be far more complex than those outlined by the standard those of the form all Xs have property Y are refutable (if false) but theory. Thus, it is not difficult to see that there are numerous obstacles in not verifiable (even if true). On the other hand, strictly existential state- the way of constructing any convincing refutation of maximization, one ments those of the form there are some Xs which have property Y are which would be beyond question. verifiable (if true) but not refutable (even if false). At first glance it would I now wish to offer some different considerations about the potential seem that the maximization hypothesis all decision-makers are maxi- refutations of the neoclassical behavioural hypothesis. I will argue here that mizers is straightforwardly a universal statement and hence is refutable even if one could prove that a consumer is not maximizing utility or a but not verifiable. But the statistical and methodological problems of producer is not maximizing profit, this would not constitute a refutation of empirical refutation present many difficulties. Some of them are well the neoclassical hypothesis. The reason why is that the actual form of the known but, as I shall show a little later, the logical problems are insur- neoclassical premise is not a strictly universal statement. Properly stated, mountable. the neoclassical premise is: For all decision-makers there is something

4 16 Principles of economics LAWRENCE A. BOLAND The neoclassical maximization hypothesis 17 they maximize. This statement has the form which is called an incomplete not a matter of logical form. The problem with the hypothesis is that it is all-and-some statement. Incomplete all-and-some statements are neither treated as a metaphysical statement. verifiable nor refutable! As a universal statement claiming to be true for all A statement which is a tautology is intrinsically a tautology. One cannot decision-makers, it is unverifiable. But, although it is a universal statement make it a non-tautology merely by being careful about how it is being used. and it should be logically possible to prove it is false when it is false (viz. A statement which is metaphysical is not intrinsically metaphysical. Its by providing a counter-example) this form of universal statement cannot be metaphysical status is a result of how it is used in a research programme. so easily rejected. Any alleged counter-example is unverifiable even if Metaphysical statements can be false but we may never know because they true! 10 are the assumptions of a research programme which are deliberately put Let me be specific. Given the premise All consumers maximize beyond question. Of course, a metaphysical assumption may be a tautology something, the critic can claim to have found a consumer who is not but that is not a necessity. maximizing anything. The person who assumed the premise is true can Typically, a metaphysical statement has the form of an existential respond: You claim you have found a consumer who is not a maximizer statement (e.g. there is class conflict; there is a price system; there is an but how do you know there is not something which he or she is invisible hand; there will be a revolution; etc.). It would be an error to think maximizing? In other words, the verification of the counter-example that because a metaphysical existential statement is irrefutable it must also requires the refutation of a strictly existential statement; and as stated be a tautology. More important, a unanimous acceptance of the truth of any above, we all agree that one cannot refute strictly existential statements. existential statement still does not mean it is a tautology. In summary, empirical arguments such as Simon s or Leibenstein s that Some theorists inadvertently create tautologies with their ad hoc deny the truth of the maximization hypothesis are no more testable than the attempts to overcome any possible informational incompleteness of their hypothesis itself. Note well, the logical impossibility of proving or theories. For example, as an explanation, global maximization implies the disproving the truth of any statement does not indicate anything about the adequacy of either the consumer s preferences or the consumer s theory of truth of that statement. The neoclassical assumption of universal all conceivable bundles which in turn implies his or her acceptance of an maximization could very well be false, but as a matter of logic we cannot unverifiable universal statement. Some theorists thus find global expect ever to be able to prove that it is. maximization uncomfortable as it expects too much of any decision-maker but the usual reaction only makes matters worse. The maximization hypothesis is easily transformed into a tautology by limiting the premise to THE IMPORTANCE OF DISTINGUISHING BETWEEN local maximization. Specifically, while the necessary conditions (a) and (b) TAUTOLOGIES AND METAPHYSICS are not sufficient for global maximization, they are sufficient for local Some economists have charged that the maximization hypothesis should be maximization. If one then changes the premise to say, if the consumer is rejected because, they argue, since the hypothesis is not testable it must maximizing over the neighbourhood of the chosen bundle, one is only then be a tautology, hence it is meaningless or unscientific. Although begging the question as to how the neighbourhood was chosen. If the they may be correct about its testability, they are wrong about its being neighbourhood is defined as that domain over which the rate of change of necessarily a tautology. Statements which are untestable are not necessarily the slope of the marginal utility curve is monotonically increasing or tautologies because they may merely be metaphysical. decreasing, then at best the hypothesis is circular. But what is more important here, if one limits the premise to local maximization, one will Distinguishing between tautologies and metaphysics severely limit the explanatory power or generality of the allegedly explained behaviour. 11 One would be better off maintaining one s Tautologies are statements which are true by virtue of their logical form metaphysics than creating tautologies to seal their defense. alone that is, one cannot even conceive of how they could ever be false. For example, the statement I am here or I am not here is true regardless of the meaning of the non-logical words I or here. There is no conceivable Metaphysics vs methodology counter-example for this tautological statement. But the maximization Sixty years ago metaphysics was considered a dirty word but today most hypothesis is not a tautology. It is conceivably false. Its truth or falsity is people realize that every explanation has its metaphysics. Every model or

5 18 Principles of economics LAWRENCE A. BOLAND The neoclassical maximization hypothesis 19 theory is merely another attempted test of the robustness of a given In summary, the general lesson to be learned here is that while it may metaphysics. Every research programme has a foundation of given seem useful to criticize what appear to be necessary elements of behavioural or structural assumptions. Those assumptions are implicitly neoclassical economics, it may not be fruitful when the proponents of ranked according to their questionability. The last assumptions on such a neoclassical economics are unwilling to accept such a line of criticism. rank-ordered list are the metaphysics of that research programme. They can External criticisms may be interesting for critical bystanders, but for even be used to define that research programme. In the case of neoclassical someone interested only in attempting to see whether it is possible to economics, the maximization hypothesis plays this methodological role. develop a neoclassical model to explain some particular economic Maximization is considered fundamental to everything; even an assumed phenomenon, the questions of interest will usually only be the ones equilibrium need not actually be put beyond question as disequilibrium in a concerning particular techniques of model-building. They will usually be market is merely a consequence of the failure of all decision-makers to satisfied with minimalist concern for whether the model as a whole is maximize. Thus, those economists who put maximization beyond question testable and thus be satisfied to say that if you think you can do better with cannot see any disequilibria. a non-neoclassical model (in particular, one which does not assume The research programme of neoclassical economics is the challenge of maximization), then you are quite welcome to try. When you are finished, finding a neoclassical explanation for any given phenomenon that is, the neoclassical economists will be willing to compare the results. Which whether it is possible to show that the phenomenon can be seen as a logical model fits the data better? But until a viable competitor is created, the consequence of maximizing behaviour thus, maximization is beyond neoclassical economists will be uninterested in a priori discussions of the question for the purpose of accepting the challenge. 12 The only question of realism of assumptions which cannot be independently tested as is the case substance is whether a theorist is willing to say what it would take to with the maximization assumption. convince him or her that the metaphysics used failed the test. For the reasons I have given above, no logical criticism of maximization can ever convince a neoclassical theorist that there is something intrinsically wrong NOTES with the maximization hypothesis. 1 Thus one might use Simon s argument to deny the necessity of the Whether maximization should be part of anyone s metaphysics is a maximization assumption. But this denial is an indirect argument. It is also somewhat unreliable. It puts the onus on the critic to offer an equally sufficient methodological problem. Since maximization is part of the metaphysics, argument that does not use maximization either explicitly or implicitly. neoclassical theorists too often employ ad hoc methodology to deflect Sometimes what might appear as a different argument can on later examination possible criticism; thus any criticism or defense of the maximization turn out to be equivalent to what it purports to replace. This is almost always hypothesis must deal with neoclassical methodology rather than the truth of the case when only one assumption is changed. the hypothesis. Specifically, when criticizing any given assumption of 2 Note that any hypothesized utility function may already have the effects of constraints built in as is the case with the Lagrange multiplier technique. maximization it would seem that critics need only be careful to determine 3 This is not the error I discussed in the previous chapter, that is, the one where whether the truth of the assumption matters. It is true that for followers of some people call (b) the sufficient condition. Friedman s Instrumentalism the truth of the assumption does not matter, 4 Although Shackle s argument applies to the assumption of either local or global hence for strictly methodological reasons it is futile to criticize maximization, it is most telling in the case of global maximization. maximization. And the reasons are quite simple. Practical success does not 5 Requiring an inductive proof of any claim to knowledge is called Inductivism. Inductivism is the view that all knowledge is logically derived generalizations require true knowledge and Instrumentalism presumes that the sole that are based ultimately only on observations. The generalizations are not objective of research in economic theory is immediate solutions to practical instantaneous but usually involve secondary assumptions which require more problems. The truth of assumptions supposedly matters to those economists observations to verify these assumptions to ensure that the foundation of who reject Friedman s Instrumentalism, but for those economists interested knowledge will be observations alone. This theory of knowledge presumes that in developing economic theory for its own sake I have argued here that it is any true claim for knowledge can be proven with singular statements of observation. Inductivism is the belief that one could actually prove that all still futile to criticize the maximization hypothesis. There is nothing swans are white by means of observing white swans and without making any intrinsically wrong with the maximization hypothesis. The only problem, if assumptions to help in the proof. It is a false theory of knowledge simply there is a problem, resides in the methodological attitude of most because there is no logic that can ever prove a strictly universal generality neoclassical economists. based solely on singular observations even when the generality is true [see

6 20 Principles of economics LAWRENCE A. BOLAND 2 Marshall s Principles and further my 1982 book, Chapter 1]. 6 Again this raises the question of the intended meaning of the maximization premise. If global maximization is the intended meaning, then the consumer must have a (theory of his or her) preference ordering over all conceivable the element of Time alternative bundles. At a very minimum, the consumer must be able to distinguish between local maxima all of which satisfy both necessary conditions, (a) and (b). 7 Some people have interpreted Simon s view to be saying that the reason why decision-makers merely satisfice is that it would be too costly to collect all the necessary information to determine the unique maximum. But this interpretation is inconsistent if it is a justification of assuming only satisficing as it would imply cost minimization which of course is just the dual of utility maximization! 8 The Slutsky Theorem is about the income and substitution effects and involves an equation derived from a utility maximization model which shows that the The Hatter was the first to break the silence. What day of the month is slope of a demand curve can be analyzed into two basic terms. One represents it? he said, turning to Alice: he had taken his watch out of his pocket, the contribution of the substitution effect to the slope and the other the income and was looking at it uneasily, shaking it every now and then, holding effect s contribution. The equation is interpreted in such a manner that all the it to his ear... terms are in principle observable. Two days wrong! sighed the Hatter. I told you butter wouldn t 9 For example, if one could show that when the income effect is positive but the suit the works! he added, looking angrily at the March Hare. demand curve is positively sloped, then the Slutsky Theorem would be false or It was the best butter, the March Hare replied. there is no utility maximization [see Lloyd 1965]. I will return to Lloyd s views Lewis Carroll of the testability of the Slutsky equation in Chapter The important point to stress here is that it is the incompleteness of the statement that causes problems. Whether one can make such statements While it might not be possible to confront neoclassical theory by criticizing verifiable or refutable depends on how one completes the statement. For example, if one completes the statement by appending assertions about the the maximization hypothesis, its main essential element, internal criticisms nature of the function being maximized (such as it being differentiable, are still not ruled out. But internal criticisms of maximization are very transitive, reflexive, etc.) one can form a more complete statement that may be difficult since too often utility as the objective of maximization is not refutable [see Mongin 1986]. directly observable. Are there any ancillary aspects of maximization that 11 See note 6 above. If one interprets maximization to mean only local maximiza- can be critically examined? Perhaps if there are, we can find them in the tion, then the question is begged as to how a consumer has chosen between competing local maxima. views that Marshall developed in his famous book Principles of Economics 12 For these reasons the maximization hypothesis might be called the paradigm [1920/49]. Marshall, I now think, had a clear understanding of the according to Thomas Kuhn s view of science. But note that the existence of a limitations of what we know as neoclassical economics. Recognized paradigm or of a metaphysical statement in any research programme is not a limitations would seem to be a good starting point for a critical psychological quirk of the researcher. Metaphysical statements are necessary examination of neoclassical economics. because we cannot simultaneously explain everything. There must be some exogenous variables or some assumptions (e.g. universal statements) in every I say that I now have this view because as a product of the 1950s and explanation whether it is scientific or not. 1960s I never learned to read originals we were taught to be in a big hurry. Consequently I accepted the many second-hand reports which alleged that the contributions of Samuelson, Hicks, Robinson, Sraffa, Keynes, Chamberlin, Triffin and others represented major or revolutionary advances in economic science which displaced the contributions of Marshall. If the truth were told, economic theory is no better off maybe it is even worse off. With respect to Marshall s Principles the only apparent accomplishment of more modern writings is a monumental obfuscation of the problem that

7 22 Principles of economics LAWRENCE A. BOLAND Marshall s Principles and the element of Time 23 Marshall s method of analysis was created to solve. A clear understanding sufficient explanation of phenomena. The Principle of Substitution of the methodological problem that concerned Marshall is absolutely presumes the truth of what Marshall calls the Principle of Continuity. Since essential for a clear understanding of the Marshallian version of Marshall wishes to apply the Principle of Substitution to everything, he neoclassical economics. Unfortunately, owing to our technically oriented needs to show that the Principle of Continuity applies to everything. In training, we have lost the ability to appreciate Marshall s approach to the simple terms, the Principle of Continuity says everything is relatively a central problem of economic analysis which is based on the methodological matter of degree. For Marshall there are no class differences, only matters role of the element of time. Having said this I do not want to lead anyone to of degree. He takes the same attitude towards the differences between city think that I am simply saying that one can understand Marshall by mulling men and ordinary people, between altruistic motives and selfish motives, over each passage of everything he wrote. Reading the history of economic between short runs and long runs, between cause and effect, between Rent thought has its limitations, too. My main interest is improving my and Interest, between man and his appliances, between productive and nonunderstanding of modern neoclassical economics, so I view historical productive labour, between capital and non-capital, and even between works as a guide rather than a rule. 1 It is my understanding that is at issue, needs and non-essentials. In all cases whether the degree in question is not Marshall s. Nevertheless, appreciating why Marshall saw problems more or less is relative to how the distinction is being used in an with the element of Time and its role in economic analysis can be a explanation. For example, what is a short period for one problem, is a long fruitful basis for a critical understanding of Marshall s version of period for another [p. vii]. 3 neoclassical economics. Sometimes it seems that Marshall is probably the only neoclassical Unlike neo-walrasian equilibrium models, which take time for granted, economist who fully appreciates the methodological problem of the Marshall s economics allows time to play a central role. 2Simply stated, the applicability of the Principle of Substitution. To be sure of its applicability, recognition of the element of time is Marshall s solution to the problem of he postpones its introduction until Book V, the fifth of six major parts of explanation which all economists face. That problem can only be his book. The first four Books are devoted to convincing the reader that the appreciated in relation to a specific explanatory principle or behavioural assumption of maximization is applicable by demonstrating the universal hypothesis. Such a relationship was introduced in the preface to Marshall s applicability of the Principle of Continuity. There must be available a first edition where he refers to the Principle of Continuity. But he explains continuous range of options 4 over which there is free choice (i.e. neither the role of continuity in the problem of explanation nor the problem substitutability is precluded whenever choice is completely limited), and itself. The problem, it turns out, results primarily from a second explan- the choice must not be an extreme (or special) case otherwise the atory principle, the Principle of Substitution, which he introduces later (in question would be begged as to what determines the constraining extreme Book V). I will argue here that Marshall saw an essential role for time in limit. economic explanations for the simple reason that he wished to apply only these two principles to all economic problems. THE ELEMENT OF TIME THE TWO EXPLANATORY PRINCIPLES Marshall stresses (e.g. in his original preface) that the applicability of the Principle of Continuity (and consequently the applicability of the Principle It seems surprising that there are only two explanatory principles stated by of Substitution) depends heavily on the element of Time. By ignoring the Marshall the Principle of Substitution and the Principle of Continuity. element of time, our teachers (and their textbooks) would have us believe These two explanatory principles are distinguished from laws (or that the Principle of Substitution is the only hypothetical aspect of the tendencies ) which also play a role in his explanations. The principles are Principles. If one could reduce everything to maximization then assumptions (we assume because we do not know) but Marshall considers explanation would certainly be made at least formally easier. Samuelson laws to be beyond doubt. saw that it was possible for even the notion of a stable equilibrium to be The Principle of Substitution is easily the more familiar of the two since reduced to the Principle of Substitution [e.g. Samuelson 1947/65, p. 5], that it is merely what we now call the neoclassical maximization hypothesis. It is, to a matter of constrained maximization. Time, if considered at all, is says, everyone is an optimizer (i.e. a maximizer or minimizer) given his or deemed relevant only for the proofs of the stability of equilibria. Most of us her situation (including his or her endowment). But by itself it is not a have been trained not to see any difficulty with the element of time for

8 24 Principles of economics LAWRENCE A. BOLAND Marshall s Principles and the element of Time 25 fear of being accused of incompetence. Marshall regards conditions as variables which are exogenously fixed Marshall s view is quite the contrary: the element of time is central. For during the period of time under consideration. He relies on their fixity in instance, to presume that at any point in time a firm has chosen the best his explanation of behaviour where these fixed variables are the constraints labour and capital mix presumes that time has elapsed since the relevant in a maximization process. In this regard, Marshall s neoclassical givens were established (viz. the technology, the prices, the market programme is indistinguishable from the mathematical approach of his conditions, etc.), and that period of time was sufficient for the firm to vary contemporary Leon Walras. However, in Walras approach, as it is taught those things over which it has control (viz. the labour hired and the capital today, the constraints are given as stocks to be allocated between purchased) prior to the decision or substitution. Even when its product s competing uses. And, of course, Walras is usually thought to consider all price has gone up the firm cannot respond immediately. Nor can it stop processes to be completed simultaneously as if the economy were a system production and its employment of labour merely because the price has of simultaneous equations. Nevertheless, although both approaches to fallen [cf. p. 298]. Contrary to modern textbooks, in Marshall s economics explanation are scientific in Marshall s sense, the mathematical concepvery short-run market pressures are more the noise than they are the tion of an economy is rejected [p. 297]. signal when viewed from the perspective of the entrepreneur s decision In Marshall s view the problem of explanation is that there are too many process. 5 conceivable causes. It is not that one has to rely on exogenous givens as Time is an essential element in Marshall s method of explanation. being causes in any hypothesized relationship, but rather that there are so Marshall tells us quite a lot about explanation in economics. He stresses the many exogenous variables to consider. This problem was not the one faced need to recognize the role of fixed conditions, but he also stresses that the by followers of Walras who are more concerned with the solvability of his fixity is not independent of the defining time periods. 6Marshall s use of system of equations. Marshall s problem was the direct result of the the term conditions can lead to confusion, so it might be useful to method he used to deal with the necessity of conditional explanations. examine his theory of explanation more specifically by distinguishing Where followers of Walras in effect try to attain the greatest generality or between dependent, independent and exogenous variables, and between scope of the explanations by maximizing the number of endogenous fixed and exogenous conditions. These distinctions crucially involve the variables and minimizing the number of exogenous variables, Marshall element of time. deliberately adopts a different strategy by attempting to maximize the The relationship between dependent and independent variables is number of fixed exogenous variables at the beginning of his analysis so as supposed to be analogous to the relationship between causes and effects. to reduce the explanation to a sequence of single-variable maximizing Marshall, however, cautions us that all such distinctions are relative. For choices. All other variables are fixed because they are exogenous givens or instance, in the very short period the market price is the dependent variable because they are exogenously fixed by a prior maximization process. The and, given the demand, the quantity supplied is the independent variable. exogenous reason that they are fixed in any problem is the logical basis for But, in the usual short run, the market price is the independent variable and, their use in his explanation. given technology (i.e. the production function), the quantity supplied is the There is a difficulty with Marshall s approach to explanation whenever dependent variable. there are many variables. It is difficult to distinguish between the In the preface to the Principles Marshall recognizes the usual type of endogenous conditions those which are exogenously fixed for the period interdependence as being an instance of the Principle of Continuity. He of time considered (e.g. fixed capital in the short run ) and the truly specifically credits Cournot with teaching us to face the difficulty of exogenous conditions that can never be explained as outcomes of a mutual determination. Marshall calls this type of interdependence a maximization process (e.g. weather, social conditions, states of knowledge, mathematical conception of continuity although he refers to this conception etc.). Although exogenous variables need not be fixed, in Marshall s only in regard to the relationship between causes and effects. 7 Today we approach they are treated as fixed by limiting the length of the period of might say that, in Marshall s short period, price and quantity are both time to which the explanation refers. endogenous variables and are simultaneously determined by the In Marshall s view, the problem of explanation is thus one of carefully exogenously given technology and demand. Thus, the distinction between defining the fixity of the conditions by defining the relevant period of independent and dependent variables is only a matter of verbal convenience time for the operation of the explanatory Principle of Substitution. Of since both are endogenous. course, what is a relevant period of time depends conversely on what are

9 26 Principles of economics LAWRENCE A. BOLAND Marshall s Principles and the element of Time 27 the relevant exogenous conditions for the application of the Principle of another aspect of the element of time. If the state of affairs at any point in Substitution. For example, in Marshall s short period a few months [p. time is to be explained as a consequence of someone s optimizing choice, it 314] virtually everything but the level of output and the amount of labour must have been possible to alter one s choices and this possibility is both employed is by definition fixed; but in his long period several years [p. a matter of the time available and the continuity of options. Needless to 315] everything but technology and social conditions is endogenous. say, it also presumes the ability to know what is the best option. Learning As with Walras economics, in Marshall s economics the truly what is the best option takes time [p. 284]. This question of learning, I exogenous variables are the only bases for explanations. Any variable would argue, is the explanatory problem involving the element of time. Of which is fixed for a period of time and which serves as a constraint on course, for Marshall, the inductive scientist, time is all that is necessary for anyone s maximization process must be explained at some stage or be the accumulation of the needed knowledge. Unlike the classical school, explicitly identified as an exogenous variable. More important, if it is not Marshall sees no need to assume perfect knowledge because he explicitly an exogenous variable, its fixity at any stage must be explained in terms of wishes to recognize the period of time under consideration a period he acceptable exogenous variables. 8 Even though Marshall s approach begins would consider sufficiently long to obtain any necessary knowledge. 10 by maximizing the number of fixed exogenous variables, his ultimate objective is, like that of the followers of Walras, to explain as much as possible. Since by definition exogenous variables are those which are to be MARSHALL S STRATEGY left unexplained, the Marshallian methodological strategy then is to reduce It would be misleading to suggest that Marshall s problem of explanation is the number of exogenous variables in stages. Marshall obviously merely a matter of defining a long-run equilibrium, for it is also a matter of considered the methodological problem of explanation in economics to be how the long-run equilibrium is reached. Again, in Marshall s view [p. solvable. 304], the explanatory problem is that there are too many exogenous In Marshall s economics the truly exogenous variables are the only variables in the short run during which most decisions are made. His causes in the strict sense. According to Marshall s view, if one is to strategy is intended to reduce the number of exogenous variables by provide a long-run explanation, time must be allowed for causes to increasing the number of variables to which the Principle of Substitution produce their effects [p. 30]. Of course, this is a source of great difficulty can be applied at later stages. 11 Marshall thus considers the problem of in economics [because] the causes themselves may have changed [p. 30]. explanation to be solvable since he recognizes that there is a different Note, however, that the changeability of causes, that is, the changeability degree of changeability for each variable (another application of the of exogenous variables, is not the problem of explanation, but rather, it is Principle of Continuity). In short, Marshall s strategy is to distinguish the more narrow methodological problem of verifying or refuting one s between short-run and long-run explanations. Any complete explanation explanation. 9 must specifically assume which variables can be changed most quickly Even when changes in the exogenous givens are assumed away, the that is, the variables must be ordered according to their changeability. fundamental problem for all explanations involving time still exists. The Different orderings may yield a different path to the long-run equilibrium. logic of explanation (for example, of all the co-determined endogenous Unless the assumption is very specific it may be impossible to distinguish variables) requires that we recognize at least one exogenous variable; and between a long-run moving equilibrium and a short-run movement toward given maximization with exogenous tastes and exogenous constraints, a new long-run equilibrium. changes in endogenous variables are explained as being caused by changes Although Marshall gives a prominent role to the distinction between in at least one of the exogenous variables. But this means that an long and short periods, it is not sufficient to solve his problem of explanation of long-run dynamic behaviour requires at least one exogenous explanation which, as I have said, is a problem concerning the variable which is impervious to the amount of real time elapsed in the long methodological choice of exogenous variables that are impervious to time. run (otherwise, the explanation might be circular). For this purpose, the Yet most commentators seem to think that Marshall s statical method explanatory element of time involves the identification of at least one time- namely, the contents of Book V constitutes his solution to the problem of independent exogenous variable that is, one which does not change over explanation. This is a mistake. the defined long run. The first point to be made is that Marshall s statical or partial It should be noted that Marshall s view of explanation also recognizes equilibrium method of analysis yields incomplete explanations. The

10 28 Principles of economics LAWRENCE A. BOLAND Marshall s Principles and the element of Time 29 statical method is relevant only for decisions on the margin or in the opposed to the short-run or long-run equilibrium price) is the only real time neighbourhood of an equilibrium position. By itself the method examines observable price. This theory of market prices assumes that the supply the necessary but not the sufficient conditions for equilibrium. The second quantity is fixed virtually everything is fixed but the price. The remainder point to be made is that Marshall does offer a more complete explanation of the discussion in Book V is an examination of what happens to the which is based on the contents of Book IV. By itself, Book V deals only market price over time when more and more of the fixed givens are with the noise in order at best to explain it away. A source of an allowed to change. For example, Marshall begins by allowing the firms to explanation of an economy s true dynamics and its application of the make substitutions in their quantity supplied in response to the current level Principle of Continuity to the element of time is to be found in Book IV. of the market price (relative to costs). This short-run process of These two points will be discussed in turn. substitution requires some time a few months or a year [p. 314]. Marshall says that he wishes to argue that demand determines the The insufficiency of Book V market price in one extreme the very short run and technology determines the market price in the other extreme the long-run I do not think Marshall ever claims that Book V alone represents a equilibrium. Implicitly the real world is somewhere in between. 13 Again, complete explanation of an economy s behaviour. Yet, judging by modern the meaning of determines is only a matter of relationships made textbooks, one could easily think that Book V is the principles of necessary by virtue of his defined equilibria. If at a point in time the economics. What we call microeconomic analysis today can all be found economy is at a long-run equilibrium, it must also be at a short-run in Book V. Nevertheless, implicitly Book V provides only the necessary equilibrium, since if it were not there would be short-run incentives to conditions for any equilibrium. That is, on the assumption that an economy change the givens which are the constraints in the determination of the is in long-run equilibrium at a point in time, certain necessary relationships market price. Similarly, the short-run equilibrium presumes that the market must hold whenever that assumption is true. It is a statical method is in equilibrium. In other words, every long-run equilibrium must also be a because it may be relevant only for that one equilibrium position at one short-run equilibrium and every short-run equilibrium must be a marketpoint in time. In effect, Book V examines the local stability properties of run equilibrium. This nesting of the forms of equilibrium is the essence of the assumed long-run equilibrium that are the logical consequences of Marshall s statical method. definitions of equilibrium and of the long period. But it will be argued Although it is now very easy to list the necessary conditions for the below that the stability properties are heavily dependent on the empirical existence of a long-run equilibrium, the key question still concerns the assertions of Book IV. sufficient conditions for the existence of a long-run equilibrium, which To be specific, before Book V can be considered relevant for anything, must be consistent with both a short-run equilibrium and a market that is, before it can play a role in economic analysis, a key question must equilibrium. The question of consistency has been a major source of be asked: why should there ever be a long-run equilibrium? Marshall controversy over the last sixty years. The logical problem is that the approaches this question in two ways. The most familiar is in Book V absence of excess profits in conjunction with profit maximization in the where he defines an ordering of the changeability of the variables with long period implies that the production function is locally linearrespect to three periods of time the very short period, the short period homogeneous (constant returns to scale on the margin); but this implication and the long period. The quickest variable in Marshall s world is the appears to be inconsistent with a downward sloping demand curve, the market-determined price. In fact, his definition of a market is not the ultimate constraint thought to be necessary to limit the size of the textbook one of a place where buyers and sellers meet to haggle over the producer. 14 price. Marshall makes the existence of a market depend on whether the Marshall s only line of defense is his other approach, which is based on price clears quickly enough for all producers to face the same price the Principle of Continuity. Given the continuous operation of the Principle regardless of their location. For Marshall then there is no market for any of Substitution, it is quite possible for the price to be above or below the good whose price is either not uniform 12 or not quickly established. In long-run equilibrium price. When it is above there are positive excess effect, this axiom about market prices makes all firms price-takers since it profits and when it is below there are losses and, logically, there must be a takes longer to establish their (short-run) decisions than the price itself. (long-run equilibrium) point in between where excess profits are zero. The Marshall s definition of the market means that the market price (as apparent inconsistency is due only to the discussion of the hypothetical and